1) In physics, a mathematical equation that predicts observed results, but has
no known theoretical basis to explain why it works.
2) In chemistry, a simple expression of the relative number of
each type of atom in a chemical compound.

1) Physics, Math.: A statement of facts in a symbolical or general form, by
substitution in which a result applicable to particular data may be obtained.
2) Chemistry: An expression of the constituents of a compound by symbols and figures.

The formula expressing the value of a → definite integral
of a given function over an interval as the difference of the values at the end
points of the interval of any → antiderivative of the
function: ∫f(x)dx = F(b) - F(a), summed from x = a to
x = b.

Named after Isaac → Newton and
Gottfried Wilhelm Leibniz (1646-1716), who both knew the rule, although it
was published later; → formula.

Nyquist formula

دیسول ِ نیکویءیست

disul-e Nyquist

Fr.: formule de Nyquist

The mean square noise voltage across a resistance in thermal equilibrium is
four times the product of the resistance, Boltzmann's constant, the absolute
temperature, and the frequency range within which the voltage is measured.
→ Johnson-Nyquist noise.

Named after Harry Nyquist (1889-1976), a Swedish-born American physicist, who made
important contributions to information theory.
→ Johnson-Nyquist noise; → formula.

Planck's blackbody formula

دیسول ِ سیه‌جسم ِ پلانک

disul-e siyah jesm-e Planck

Fr.: formule du corps noir de Planck

A formula that determines the distribution of intensity of radiation
that prevails under conditions of thermal equilibrium at a temperature
T:
Bv = (2hν3 / c2)[exp(hν / kT) - 1]-1
where h is Planck's constant
and ν is the frequency.

A → semiempirical → equation
which describes the → binding energy
of the → atomic nucleus. It is essentially a nuclear mass formula
that provides the total binding energy per → nucleon as the sum
of five terms:
Eb = aVA - aSA2/3 -
aCZ2/A1/3 -
aA(N -Z)2/A + δ(A,Z),
where the terms in the right-hand side of this equation are called the volume
term, surface term, Coulomb term, asymmetry term, and pairing term, respectively.
A, Z, and N are
the number of nucleons, → protons, and
→ neutrons, respectively
(see, e.g., Alexi M. Frolov, 2013, arxiv.org/pdf/1212.6768). Also called
Bethe-Weizacker formula and
→ semiempirical binding energy formula.